Related papers: p-Adic Heisenberg Cantor sets, 3

In these informal notes, we continue to explore p-adic versions of Heisenberg groups and some of their variants, including the structure of the corresponding Cantor sets.

A basic class of constructions is considered, in connection with bilipschitz mappings in particular.

These informal notes deal with p-adic versions of Heisenberg groups and related matters.

A class of solenoids is considered, including some aspects in n (topological) dimensions, where one basically gets some fractal versions of tori.

We construct a Cantor set in S^3 whose complement admits a complete hyperbolic metric.

In this paper we survey $n$-dimensional solenoidal manifolds for $n=1,2$ and 3, and present new results about them. Solenoidal manifolds of dimension $n$ are metric spaces locally modeled on the product of a Cantor set and an open…

We consider compact, aspherical solenoids obtained as the inverse limit of a system of CW~complexes and covering maps. This includes $P$-adic solenoids, as well as the universal hyperbolic solenoid of Teichm\"{u}ller theory. Using ideas…

This paper will be splited into two papers and submited later.

Collection of (equivariant) $\rm{PL}$-mappings admitting a relative abelian, cyclic, quaternionic, bicyclic, and quaternionic-cyclic structures are constructed.

A class of Cantor-type spaces and related geometric structures are discussed.

In this paper we discuss several variations and generalizations of the Cantor set and study some of their properties. Also for each of those generalizations a Cantor-like function can be constructed from the set. We will discuss briefly the…

We study limit mappings from a solenoid onto itself. It is shown that each equivalence class of finite-sheeted covering mappings from connected topological spaces onto a solenoid is determined by a limit mapping. Properties of periodic…

When a solenoid is embedded in three space, its complement is an open three manifold. We discuss the geometry and fundamental groups of such manifolds, and show that the complements of different solenoids (arising from different inverse…

Here we report on observations of the three-dimensional structure of a sunspot magnetic field from the photosphere to the chromosphere, obtained with the new visible/infrared spectro-polarimeter SPINOR. The observations, interpreted with a…

A basic family of solenoids is discussed, especially from the point of view of analysis on metric spaces.

Some aspects of multidimensional soliton geometry are considered.

We considered real, p-adic and adelic noncommutative scalar solitons and obtained some new results.

This chapter describes interrelations between: (1) algebraic structure on sets of scalars, (2) properties of monads associated with such sets of scalars, and (3) structure in categories (esp. Lawvere theories) associated with these monads.…

We find all Heegaard diagrams with the property "alternating" or "weakly alternating" on a genus two orientable closed surface. Using these diagrams we give infinitely many genus two 3--manifolds, each admits an automorphism whose…

Helical solenoids have been proposed as an option for a Helical Cooling Channel for muons in a proposed Muon Collider. Helical solenoids can provide the required three main field components: solenoidal, helical dipole, and a helical…